$F(5) = F(4) + F(2) + 1$
$F(4) = F(3) + F(1) + 1$
$F(3) = F(2) + F(0) + 1$
Hence, Solving all gives $F(5) = 7$ with $3$ distinct invocations.
$F(7) = F(6) + F(4) + 1$
$F(6) = F(5) + F(3) + 1$
$F(5) = F(4) + F(2) + 1$
$F(4) = F(3) + F(1) + 1$
$F(3) = F(2) + F(0) + 1$
And, Solving all gives $F(7) = 17$ with $8$ invocations, assuming there is no saving in the above code.
Or,